I am wondering if a FPS (or any game in first person perspective for that matter) exists that incorporates the rotation of the player's head.
Most FPSs simply rotate the camera as the player turns, but it would be more realistic if the camera rotated relative to a joint that would be positioned somewhere where the character's neck would be.
At least the pitch could be adapted to this method of camera rotation without much alteration to the game. If you would also want to do it for yaw, you'd need to make a threshold where turning the head transitions into turning the body. (Note how most FPSs out there now will rotate the entire character when the player turns left or right, instead of just the head.)
Also, if you have done experiments with this method of camera rotation, could you please share your results? (I can imagine it doesn't exist in any games yet because it is annoying or disorienting. )

Making controls for such a game would be very difficult. How do you rotate the head and then the arms to bring a weapon to bear?

The closest I could think of are the mechwarrior-type games. However, as the 'mech torso twists, the weapons still track with the user's point of view.

The best way to make this work would be to ensure that the system would work with a head mounted display (VR goggles) and that the weapon/controller would be directly operated as they would in game, sort of like the wiimote gun.

I don't think there are any consumer level games out there that achieve this, however, I believe there are serious games out there that may.

Of course, if you're a stickler for tactical detail, your weapon's barrel should always be pointing where you're looking anyway, so the way FPS games currently operate is pretty realistic.

Well, let's abandon the FPS genre for a moment. We're still in first person, but there is no gun. (Or perhaps you can shoot lasers from your eyes or something... :P). What I'm interested in is not the actual turning of the head in a game, but the subtle changes in perspective that come with it.
Just turn your head from left to right. (Like, your actual head. Do it.) Notice how objects at various distances move sideways at disproportiate rates. You could see it as real-life parallax scrolling. Going back to all the FPSs I've ever played, this never happens. Rotating the player character will rotate the camera around the point where the camera is positioned (or perhaps where the camera's projection field is situated? I've never been good at the theory of 3D projections...), which will result in a lack of this parallax scrolling-like effect.
Maybe I should just get off my lazy ass and implement it myself. :P

Perhaps the best way to implement this would be something akin to the system shown in this video: http://uk.youtube.com/watch?v=Jd3-eiid-Uw
If you were to have a fairly standard FPS (or FPnonS) but put this in and run it on a big enough monitor that is quite close up it should work pretty well for a lot of head motions, albeit not rotation beyond a certain point. Good luck, I wish I could do this kind of thing myself!